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Representation of continuous linear forms on the set of ladlag processes and the pricing of American claims under proportional costs

Bouchard, Bruno; Chassagneux, Jean-François (2009), Representation of continuous linear forms on the set of ladlag processes and the pricing of American claims under proportional costs, Electronic Journal of Probability, 14, paper numéro 24, p. 612-632. http://dx.doi.org/10.1214/EJP.v14-625

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Type
Article accepté pour publication ou publié
Date
2009
Nom de la revue
Electronic Journal of Probability
Volume
14
Numéro
paper numéro 24
Éditeur
Institute of Mathematical Statistics
Pages
612-632
Identifiant publication
Métadonnées
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Auteur(s)
Bouchard, Bruno
Chassagneux, Jean-François
Résumé (EN)
We discuss a d-dimensional version (for làdlàg optional processes) of a duality result by Meyer (1976) between {bounded} càdlàg adapted processes and random measures. We show that it allows to establish, in a very natural way, a dual representation for the set of initial endowments which allow to super-hedge a given American claim in a continuous time model with proportional transaction costs. It generalizes a previous result of Bouchard and Temam (2005) who considered a discrete time setting. It also completes the very recent work of Denis, De Vallière and Kabanov (2008) who studied càdlàg American claims and used a completely different approach.
Mots-clés
American options; Mathematical Finance; transaction costs